Subgroups — C₁₉×C₂²⋊(C₃₁⋊C₉) #35234355

Order 21204.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₉×C₃₁	C₃	1	1	yes	maximal, characteristic
2	C₁₉×C₃₁⋊C₉	—	4	1	no	maximal, Hall
3	C₂×C₃×C₁₉×C₃₁	—	3	1	no	—
4	C₂²×C₁₉×C₃₁	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₃₁	A₄	1	1	yes	characteristic
6	C₂×C₁₉×C₃₁	—	3	1	no	—
7	C₂²⋊(C₃₁⋊C₉)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₉×C₂²⋊C₉	—	31	1	no	maximal, Hall
9	C₁₉×C₃₁	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
10	C₂²×C₃×C₃₁	C₃×C₁₉	1	1	yes	characteristic
11	C₃₁⋊C₉	—	4	1	no	Hall
12	C₂²×C₃×C₁₉	C₃₁⋊C₃	1	1	yes	characteristic
13	C₂×C₃×C₃₁	—	3	1	no	—
14	C₉×C₁₉	—	124	1	no	Hall
15	C₂²×C₃₁	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₉	—	3	1	no	—
17	C₃×C₃₁	A₄×C₁₉	1	1	yes	characteristic
18	C₂²×C₁₉	C₃₁⋊C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃₁	—	3	1	no	—
20	C₃×C₁₉	C₂²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
21	C₂×C₁₉	—	3	1	no	—
22	C₂²⋊C₉	—	31	1	no	Hall
23	C₃₁	C₁₉×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
24	C₁₉	C₂²⋊(C₃₁⋊C₉)	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃	C₁₉×C₃₁⋊C₃	1	1	yes	characteristic
26	C₉	—	124	1	no	Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂²	C₁₉×C₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₁₉×C₂²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
30	C₂	—	3	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.